From (Quantified) Boolean Formulas to Answer Set Programming

We propose in this article a translation from Quantified Boolean Formulae to Answer Set Programming. The computation of a solution of a Quantified Boolean Formula is then equivalent to the computation of a stable model for a normal logic program. The case of unquantified Boolean formulae is also considered since it is equivalent to the case of Quantified Boolean Formulae with only existential quantifiers

Testing formula satisfaction

We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size

Efficiently Integrating Boolean Reasoning and Mathematical Solving

Many real-world problems require the ability of reasoning efficiently on formulae which are boolean combinations of boolean and unquantified mathematical propositions. This task requires a fruitful combination of efficient boolean reasoning and mathematical solving capabilities. SAT tools and mathematical reasoners are respectively very effective on one of these activities each, but not on both. In this paper we present a formal framework, a generalized algorithm and architecture for integrating boolean reasoners and mathematical solvers so that they can efficiently solve boolean combinations of boolean and unquantified mathematical propositions. We describe many techniques to optimize this integration, and highlight the main requirements for SAT tools and mathematicalsolvers to maximize the benefits of their integration

Boolean Propagation Based on Literals for Quantified Boolean Formulae

This paper proposes a new set of propagation rules for quantified Boolean formulae based on literals and generated automatically thanks to quantified Boolean formulae certificates. Different decompositions by introduction of existentially quantified variables are discussed in order to construct complete systems. This set of rules is compared with already proposed quantified Boolean propagation rule sets and Stålmarck\u27s method

From (Quantified) Boolean Formulae to Answer Set Programming

We propose in this article a translation from quantified Boolean formulae to answer set programming. The computation of a solution of a quantified Boolean formula is then equivalent to the computation of a stable model for a normal logic program. The case of unquantified Boolean formulae is also considered since it is equivalent to the case of quantified Boolean formulae with only existential quantifiers

Constructing Conditional Plans by a Theorem-Prover

The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and present experimental results obtained with a theorem-prover